Refined and l-adic Euler characteristics of nearly perfect complexes

Syntomic complexes and $p$-adic étale Tate twists

The primary goal of this paper is to identify syntomic complexes with the $p$-adic étale Tate twists of Geisser--Schneider--Sato on regular $p$-torsionfree schemes. Our methods apply naturally to a broader class of schemes that we call "$F$-smooth". The $F$-smoothness of regular schemes leads to new results on the absolute prismatic cohomology of regular schemes.

完美复形与完备化

Perfect complexes and completion

本文给出了交换环 $I$-进完备化上完美复形范畴与 $I$-完备复形导出范畴中可对偶化对象子范畴等价的充分必要条件，并统一恢复了诺特局部环情形下 Benson 等人的近期结果。

Refined unramified cohomology of schemes

We introduce the notion of refined unramified cohomology of algebraic schemes and prove comparison theorems that identify some of these groups with cycle groups. This recovers for cycles of low codimensions on smooth projective varieties previous results of Bloch--Ogus, Colliot-Thélène--Voisin, Kahn, Voisin, and Ma. We combine our approach with the Bloch--Kato conjecture, proven by Voevodsky, to show that on a smooth complex projective variety, any homologically trivial torsion cycle with trivial Abel--Jacobi invariant has coniveau 1. This establishes a torsion version of a conjecture of Janns…

晶性对于syntomic上同调、etale上同调和代数K-理论

Crystallinity for syntomic cohomology, étale cohomology, and algebraic $K$-theory

本文证明了模(p^c,v_1^{p^n})的syntomic上同调的晶性，并计算了代数K-理论和etale上同调的结构，同时加强了p-进收敛定理。

关于光滑方案在截断Witt向量上的代数K-理论

On the algebraic $K$-theory of smooth schemes over truncated Witt vectors

本文研究了光滑方案在截断Witt向量上的代数K-理论，引入了新的复形和微分动机复形，并通过Chern字符同构建立了K-理论微分变形的判据，与Emerton的p进变分Hodge猜想相关。